C₁₇×#13439 #16871183

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13439

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂²×C₁₇×D₁₆	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#405 ◁ G

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,35)(25,29)(26,41)(27,44)(28,34)(30,36)(31,39)(32,42)(33,40)(37,52)(38,48)(43,47)(45,50)(46,53)(49,51);(23,29)(24,36)(25,39)(26,42)(27,40)(31,33)(32,44)(34,41)(35,45)(37,53)(38,43)(46,49)(48,52)(50,51);(19,21)(22,24,25,36,40,50,42,53,28,38,26,43,27,37,39,51)(23,30,31,35,44,49,41,52,34,47,32,48,33,46,29,45)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6427);